As the title says. The item is circled and crossed out with a red circle and slash, and the recipe is "E-locomotive-power provider" and 5 seconds. It also says "Products:" and lists 2 Accumulators and 1 Advanced circuit.

I had a working system with lots of electric trains, until the new update; the new update not only stole away all my electric trains, but now there's apparently no way to power them.

what do you mean with "stole away all my electric trains". I changed the behavior of this mod. Now you dont need the power provider anymore. At the moment you only need one building, this control station.
For future updates, i will add more control stations to supply the trains (e.g. mk1 can supply 2 trains, mk2 4.....). The problem was that many user only build one power supplier for many trains and this works without much negative impact (e.g. slow trains). Now each train (locomotive entity) got a seperat hidden power supplier (you can see thah at the electricity statistics)

When I updated to Factorio 0.17, all my trains disappeared because the tech tree changed and I "hadn't researched them yet." I had 11 trains and all of them were poofed into nothingness by the update.

Thanks for the reply; I didn't realize that I need a control station rather than the E-locomotive-power provider. I'll build that and see how that goes.